Nano-lens diffraction around a single heated nano particle

Abstract

The action of a nanoscopic spherically symmetric refractive index profile on a focused Gaussian beam may easily be envisaged as the action of a phase-modifying element, i.e. a lens: Rays traversing the inhomogeneous refractive index field n(r) collect an additional phase along their trajectory which advances or retards their phase with respect to the unperturbed ray. This lens-like action has long been understood as being the mechanism behind the signal of thin sample photothermal absorption measurements [Appl. Opt. 34, 41-50 (1995)], [Jpn. J. Appl. Phys. 45, 7141-7151 (2006)], where a cylindrical symmetry and a different lengthscale is present. In photothermal single (nano-)particle microscopy, however, a complicated, though prediction-wise limited, electrodynamic scattering treatment was established [Phys. Rev. B 73, 045424 (2006)] during the emergence of this new technique. Our recent study [ACS Nano, DOI: 10.1021/nn300181h] extended this approach into a full ab-initio model and showed for the first time that the mechanism behind the signal, despite its nanoscopic origin, is also the lens-like action of the induced refractive index profile only hidden in the complicated guise of the theoretical generalized Mie-like framework. The diffraction model proposed here yields succinct analytical expressions for the axial photothermal signal shape and magnitude and its angular distribution, all showing the clear lens-signature. It is further demonstrated, that the Gouy-phase of a Gaussian beam does not contribute to the relative photothermal signal in forward direction, a fact which is not easily evident from the more rigorous EM treatment. The presented model may thus be used to estimate the signal shape and magnitude in photothermal single particle microscopy.

Reduction of distortion in photothermal microscopy and its application to the high-resolution three-dimensional imaging of nonfluorescent tissues

“…3(a)]. This can be explained by the lens-like model, where the probe beam is focused or defocused depending on the sample position and the twin peaks become asymmetric in the presence of the focal plane offset [9][10][11]. The positive peak (in-phase) is larger than the negative (180° out of phase) peak at Δz = 0 μm.…”

“…This results in local refractive index changes and induces the deflection of the probe beam. In the forward detection scheme, the nano-lens (thermal lens) effect produces positive and negative peaks corresponding to the focusing or defocusing of the probe beam when a sample is scanned in the axial direction [9][10][11]. This signal shape would be useful in the tracking or positioning of nanomaterials, but it causes a serious problem in biological imaging, as the twin peaks result create distortion when reconstructing an image of a structured sample.…”

Photothermal Microscopy for High Sensitivity and High Resolution Absorption Contrast Imaging of Biological Tissues

“…The pump beam increases the temperature, ΔT, around the focal point of the optical absorbing sample, which results in variations in the local refractive index (typically Δn ~ 10 −4 with ΔT = 1 K). Variation in the refractive index induces the deflection of the probe beam, which can be theoretically described by the Lorentz-Mie or the diffraction model [15,16]. The magnitude of the relative intensity change of the probe beam due to PT effect ΔI/I is estimated to be ~10 −4 when Δn ~ 10 −3 -10 −4 .…”

“…However, the axial PSF in PT microscopy is not the product of the pump and probe intensities. In PT microscopy with the forward detection, thermal nano-lens (thermal lens) effect produces positive and negative peaks corresponding to the focusing or defocusing of the probe beam when a sample is scanned in the axial direction [6,15,21]. This signal shape causes a serious problem in biological imaging, as the twin peaks cause distortion when reconstructing an image of a thick sample.…”

Imaging nano-objects by linear and nonlinear optical absorption microscopies

“…[5,18] In these experiments heat transfer from the particle to the surroundings creates a nano-lens that affects the propagation of the probe beam, and changes the intensity of the probe at the detector. [9, [140][141][142] The signal in PHI depends the linear absorption of the sample, in contrast to TAM which depends on the non-linear susceptibility. Because PHI relies on efficient heat transfer to the surroundings, it is typically not used to study fluorescent nanoparticles with high quantum yields.…”